using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
//ピースごとの配置候補
static Dictionary<char, List<bool[, ,]>> HaitiKouhoListDict =
new Dictionary<char, List<bool[, ,]>>();
static char[] PieceNameArr = { '1', '2', '3', '4', '5', '6' };
const int UB = 3;
struct JyoutaiDef
{
internal char[, ,] BanArr;
internal int CurrX;
internal int CurrY;
internal int CurrZ;
internal int PieceCnt;
internal int PassCnt;
internal char PrevPiece;
}
static void Main()
{
var sw = System.Diagnostics.Stopwatch.StartNew();
foreach (char EachPiece in PieceNameArr) {
HaitiKouhoListDict[EachPiece] = DeriveHaitiKouhoList(EachPiece);
}
//回転解の除外
HaitiKouhoListDict['4'].RemoveRange(1, HaitiKouhoListDict['4'].Count - 1);
var Stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.BanArr = new char[UB + 1, UB + 1, UB + 1];
for (int X = 0; X <= UB; X++)
for (int Y = 0; Y <= UB; Y++)
for (int Z = 0; Z <= UB; Z++)
WillPush.BanArr[X, Y, Z] = ' ';
WillPush.CurrX = WillPush.CurrY = WillPush.CurrZ = 0;
WillPush.PieceCnt = 0;
WillPush.PassCnt = 0;
WillPush.PrevPiece = '\0';
Stk.Push(WillPush);
while (Stk.Count > 0) {
JyoutaiDef Popped = Stk.Pop();
//クリア判定
if (Popped.PieceCnt == 6) {
Console.WriteLine("解を発見。経過時間={0}", sw.Elapsed);
PrintBan(Popped.BanArr);
break;
}
//X座標の繰上げ処理
if (Popped.CurrX > UB) {
Popped.CurrX = 0;
Popped.CurrY++;
}
//最終行を超えた場合
if (Popped.CurrY > UB) {
Popped.CurrY = 0;
//最終高さを超えた場合
if (++Popped.CurrZ > UB) continue;
}
//使用済のピース名の配列
char[] UsedPieceArr = Popped.BanArr.Cast<char>().Distinct().ToArray();
//Z=0の面で、4*4のピースを最低でも2つは使う必要あり
if (Popped.CurrZ == 1) {
int wkCnt = UsedPieceArr.Count(A => A != '3');
if (wkCnt < 2) continue;
}
int[] HabaArr = new int[3];
HabaArr[0] = UB - Popped.CurrX + 1;
HabaArr[1] = UB - Popped.CurrY + 1;
HabaArr[2] = UB - Popped.CurrZ + 1;
Array.Sort(HabaArr);
foreach (char EachPiece in PieceNameArr) {
if (Array.IndexOf(UsedPieceArr, EachPiece) >= 0) continue;
//配置可能な幅があるかをチェック
if (EachPiece == '3') {
if (HabaArr[1] < 3) continue;
}
else if (HabaArr[1] < 4) continue;
if (HabaArr[2] < 4) continue;
//ピースの配置順序を固定
if (Popped.PrevPiece != '\0' && Popped.PrevPiece >= EachPiece) continue;
//ピースの配置候補リスト
List<bool[, ,]> HaitiKouhoList = new List<bool[, ,]>();
HaitiKouhoList.AddRange(HaitiKouhoListDict[EachPiece]);
//マス目にピースを埋めれない候補をRemove
HaitiKouhoList.RemoveAll(X =>
CanFillPiece(X, Popped.CurrX, Popped.CurrY, Popped.CurrZ, Popped.BanArr) == false);
//ピースを配置する経路のPush処理
foreach (bool[, ,] EachPieceMap in HaitiKouhoList) {
WillPush.BanArr = (char[, ,])Popped.BanArr.Clone();
WillPush.CurrX = Popped.CurrX;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
WillPush.PieceCnt = Popped.PieceCnt + 1;
WillPush.PassCnt = Popped.PassCnt;
WillPush.PrevPiece = EachPiece;
for (int X = 0; X <= EachPieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= EachPieceMap.GetUpperBound(1); Y++) {
for (int Z = 0; Z <= EachPieceMap.GetUpperBound(2); Z++) {
if (EachPieceMap[X, Y, Z] == false) continue;
WillPush.BanArr[Popped.CurrX + X, Popped.CurrY + Y, Popped.CurrZ + Z]
= EachPiece;
}
}
}
Stk.Push(WillPush);
}
}
//ピースを配置しない経路のPush
if (Popped.BanArr[Popped.CurrX, Popped.CurrY, Popped.CurrZ] == ' ') {
//空き体積で枝切り
WillPush.PassCnt = Popped.PassCnt + 1;
if (WillPush.PassCnt + 8 + 10 + 9 + 11 + 9 + 9 > 4 * 4 * 4)
continue;
}
else {
WillPush.PassCnt = Popped.PassCnt;
}
WillPush.BanArr = Popped.BanArr;
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
WillPush.PieceCnt = Popped.PieceCnt;
WillPush.PrevPiece = '\0';
Stk.Push(WillPush);
}
}
//ピース名を引数として、回転させた配置のListを返す
static List<bool[, ,]> DeriveHaitiKouhoList(char pPieceName)
{
bool[, ,] wkArr = null;
Action<int, int> FillAct = (pX, pY) => wkArr[pX, pY, 0] = true;
// ■
// ■■
//■■■■
// ■
if (pPieceName == '1') {
wkArr = new bool[4, 4, 1];
FillAct(1, 0);
FillAct(1, 1); FillAct(2, 1);
FillAct(0, 2); FillAct(1, 2); FillAct(2, 2); FillAct(3, 2);
FillAct(3, 3);
}
// ■
//■■■■
// ■■■
// ■ ■
if (pPieceName == '2') {
wkArr = new bool[4, 4, 1];
FillAct(1, 0);
FillAct(0, 1); FillAct(1, 1); FillAct(2, 1); FillAct(3, 1);
FillAct(1, 2); FillAct(2, 2); FillAct(3, 2);
FillAct(1, 3); FillAct(3, 3);
}
//■ ■
//■■■
// ■■
//■■
if (pPieceName == '3') {
wkArr = new bool[3, 4, 1];
FillAct(0, 0); FillAct(2, 0);
FillAct(0, 1); FillAct(1, 1); FillAct(2, 1);
FillAct(1, 2); FillAct(2, 2);
FillAct(0, 3); FillAct(1, 3);
}
//■ ■■
//■■■
//■■■
//■ ■
if (pPieceName == '4') {
wkArr = new bool[4, 4, 1];
FillAct(0, 0); FillAct(2, 0); FillAct(3, 0);
FillAct(0, 1); FillAct(1, 1); FillAct(2, 1);
FillAct(0, 2); FillAct(1, 2); FillAct(2, 2);
FillAct(0, 3); FillAct(2, 3);
}
// ■■
//■■■
// ■■■
// ■
if (pPieceName == '5') {
wkArr = new bool[4, 4, 1];
FillAct(2, 0); FillAct(3, 0);
FillAct(0, 1); FillAct(1, 1); FillAct(2, 1);
FillAct(1, 2); FillAct(2, 2); FillAct(3, 2);
FillAct(1, 3);
}
// ■■
// ■■
//■■■■
// ■
if (pPieceName == '6') {
wkArr = new bool[4, 4, 1];
FillAct(1, 0); FillAct(2, 0);
FillAct(1, 1); FillAct(2, 1);
FillAct(0, 2); FillAct(1, 2); FillAct(2, 2); FillAct(3, 2);
FillAct(1, 3);
}
return DeriveKaitenArrList(wkArr);
}
//配列を引数として、回転させた配列のリストをDistinctして返す
static List<bool[, ,]> DeriveKaitenArrList(bool[, ,] pBaseArr)
{
var KaitenArrList = new List<bool[, ,]>();
int BaseUB_X = pBaseArr.GetUpperBound(0);
int BaseUB_Y = pBaseArr.GetUpperBound(1);
int BaseUB_Z = pBaseArr.GetUpperBound(2);
for (int I = 1; I <= 48; I++) KaitenArrList.Add(null);
for (int P = 0; P <= 7; P++) KaitenArrList[P] = new bool[BaseUB_X + 1, BaseUB_Y + 1, BaseUB_Z + 1];
for (int P = 8; P <= 15; P++) KaitenArrList[P] = new bool[BaseUB_X + 1, BaseUB_Z + 1, BaseUB_Y + 1];
for (int P = 16; P <= 23; P++) KaitenArrList[P] = new bool[BaseUB_Y + 1, BaseUB_X + 1, BaseUB_Z + 1];
for (int P = 24; P <= 31; P++) KaitenArrList[P] = new bool[BaseUB_Y + 1, BaseUB_Z + 1, BaseUB_X + 1];
for (int P = 32; P <= 39; P++) KaitenArrList[P] = new bool[BaseUB_Z + 1, BaseUB_X + 1, BaseUB_Y + 1];
for (int P = 40; P <= 47; P++) KaitenArrList[P] = new bool[BaseUB_Z + 1, BaseUB_Y + 1, BaseUB_X + 1];
for (int X = 0; X <= BaseUB_X; X++) {
for (int Y = 0; Y <= BaseUB_Y; Y++) {
for (int Z = 0; Z <= BaseUB_Z; Z++) {
bool SetVal = pBaseArr[X, Y, Z];
KaitenArrList[0][X, Y, Z] = SetVal;
KaitenArrList[1][X, Y, BaseUB_Z - Z] = SetVal;
KaitenArrList[2][X, BaseUB_Y - Y, Z] = SetVal;
KaitenArrList[3][X, BaseUB_Y - Y, BaseUB_Z - Z] = SetVal;
KaitenArrList[4][BaseUB_X - X, Y, Z] = SetVal;
KaitenArrList[5][BaseUB_X - X, Y, BaseUB_Z - Z] = SetVal;
KaitenArrList[6][BaseUB_X - X, BaseUB_Y - Y, Z] = SetVal;
KaitenArrList[7][BaseUB_X - X, BaseUB_Y - Y, BaseUB_Z - Z] = SetVal;
KaitenArrList[8][X, Z, Y] = SetVal;
KaitenArrList[9][X, Z, BaseUB_Y - Y] = SetVal;
KaitenArrList[10][X, BaseUB_Z - Z, Y] = SetVal;
KaitenArrList[11][X, BaseUB_Z - Z, BaseUB_Y - Y] = SetVal;
KaitenArrList[12][BaseUB_X - X, Z, Y] = SetVal;
KaitenArrList[13][BaseUB_X - X, Z, BaseUB_Y - Y] = SetVal;
KaitenArrList[14][BaseUB_X - X, BaseUB_Z - Z, Y] = SetVal;
KaitenArrList[15][BaseUB_X - X, BaseUB_Z - Z, BaseUB_Y - Y] = SetVal;
KaitenArrList[16][Y, X, Z] = SetVal;
KaitenArrList[17][Y, X, BaseUB_Z - Z] = SetVal;
KaitenArrList[18][Y, BaseUB_X - X, Z] = SetVal;
KaitenArrList[19][Y, BaseUB_X - X, BaseUB_Z - Z] = SetVal;
KaitenArrList[20][BaseUB_Y - Y, X, Z] = SetVal;
KaitenArrList[21][BaseUB_Y - Y, X, BaseUB_Z - Z] = SetVal;
KaitenArrList[22][BaseUB_Y - Y, BaseUB_X - X, Z] = SetVal;
KaitenArrList[23][BaseUB_Y - Y, BaseUB_X - X, BaseUB_Z - Z] = SetVal;
KaitenArrList[24][Y, Z, X] = SetVal;
KaitenArrList[25][Y, Z, BaseUB_X - X] = SetVal;
KaitenArrList[26][Y, BaseUB_Z - Z, X] = SetVal;
KaitenArrList[27][Y, BaseUB_Z - Z, BaseUB_X - X] = SetVal;
KaitenArrList[28][BaseUB_Y - Y, Z, X] = SetVal;
KaitenArrList[29][BaseUB_Y - Y, Z, BaseUB_X - X] = SetVal;
KaitenArrList[30][BaseUB_Y - Y, BaseUB_Z - Z, X] = SetVal;
KaitenArrList[31][BaseUB_Y - Y, BaseUB_Z - Z, BaseUB_X - X] = SetVal;
KaitenArrList[32][Z, X, Y] = SetVal;
KaitenArrList[33][Z, X, BaseUB_Y - Y] = SetVal;
KaitenArrList[34][Z, BaseUB_X - X, Y] = SetVal;
KaitenArrList[35][Z, BaseUB_X - X, BaseUB_Y - Y] = SetVal;
KaitenArrList[36][BaseUB_Z - Z, X, Y] = SetVal;
KaitenArrList[37][BaseUB_Z - Z, X, BaseUB_Y - Y] = SetVal;
KaitenArrList[38][BaseUB_Z - Z, BaseUB_X - X, Y] = SetVal;
KaitenArrList[39][BaseUB_Z - Z, BaseUB_X - X, BaseUB_Y - Y] = SetVal;
KaitenArrList[40][Z, Y, X] = SetVal;
KaitenArrList[41][Z, Y, BaseUB_X - X] = SetVal;
KaitenArrList[42][Z, BaseUB_Y - Y, X] = SetVal;
KaitenArrList[43][Z, BaseUB_Y - Y, BaseUB_X - X] = SetVal;
KaitenArrList[44][BaseUB_Z - Z, Y, X] = SetVal;
KaitenArrList[45][BaseUB_Z - Z, Y, BaseUB_X - X] = SetVal;
KaitenArrList[46][BaseUB_Z - Z, BaseUB_Y - Y, X] = SetVal;
KaitenArrList[47][BaseUB_Z - Z, BaseUB_Y - Y, BaseUB_X - X] = SetVal;
}
}
}
//Distinctする
for (int I = KaitenArrList.Count - 1; 0 <= I; I--) {
for (int J = 0; J <= I - 1; J++) {
//UBが違う場合は、同一でない
if (KaitenArrList[I].GetUpperBound(0) != KaitenArrList[J].GetUpperBound(0)) continue;
if (KaitenArrList[I].GetUpperBound(1) != KaitenArrList[J].GetUpperBound(1)) continue;
if (KaitenArrList[I].GetUpperBound(2) != KaitenArrList[J].GetUpperBound(2)) continue;
IEnumerable<bool> wkEnum1 = KaitenArrList[I].Cast<bool>();
IEnumerable<bool> wkEnum2 = KaitenArrList[J].Cast<bool>();
if (wkEnum1.SequenceEqual(wkEnum2) == false) continue;
KaitenArrList.RemoveAt(I);
break;
}
}
return KaitenArrList;
}
//マス目にピースを埋めれるか
static bool CanFillPiece(bool[, ,] pPieceMap,
int pTargetX, int pTargetY, int pTargetZ, char[, ,] pBanArr)
{
if (pTargetX + pPieceMap.GetUpperBound(0) > UB) return false;
if (pTargetY + pPieceMap.GetUpperBound(1) > UB) return false;
if (pTargetZ + pPieceMap.GetUpperBound(2) > UB) return false;
for (int X = 0; X <= pPieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
for (int Z = 0; Z <= pPieceMap.GetUpperBound(2); Z++) {
if (pPieceMap[X, Y, Z]
&& pBanArr[pTargetX + X, pTargetY + Y, pTargetZ + Z] != ' ')
return false;
}
}
}
return true;
}
//解を出力
static void PrintBan(char[, ,] pBanArr)
{
var sb = new System.Text.StringBuilder();
for (int Z = 0; Z <= UB; Z++) {
sb.AppendFormat("Z={0}の平面", Z);
sb.AppendLine();
for (int Y = 0; Y <= UB; Y++) {
for (int X = 0; X <= UB; X++) {
sb.Append(pBanArr[X, Y, Z] == ' ' ? '/' : pBanArr[X, Y, Z]);
}
sb.AppendLine();
}
}
Console.WriteLine(sb.ToString());
}
}
6個のピースは下記となります。 各ピースは回転や裏返しても使えます。